The present invention is applied to flight management systems for aircraft with or without an onboard pilot. Such systems, termed FMS (“Flight Management System”), ensure piloting assistance functions for determining the route to be followed by the aircraft so as to home in on its destination from its departure point while taking into account the constraints of a regulatory and operational nature to be complied with, and especially constraints relating to time of flypast and of arrival at destination.
The movements of aircraft between a departure airport and a destination airport form the subject of preparation leading to the formulation of a more or less detailed administrative document called the flight plan which assembles a collection of details relevant to the progress of the flight. This flight plan is established, firstly, for the benefit of the air traffic control authorities (airports, air traffic controls, authorities, etc.). It mentions, among other information, the identity and the type of the aircraft, as well as a summary definition of the scheduled route listing a string of waypoints linking the takeoff runway used at the departure airport to the landing runway scheduled at the destination airport, overflight constraints associated with the waypoints, the scheduled times of overflight of the waypoints, as well as optionally, the regulatory procedures for the approach followed on departure and on arrival and the air corridors employed.
The piloting of an aircraft is increasingly automated. It is performed by altering the orientations of movable surfaces (aerofoils, flaps, etc.) and altering the output of the engine or engines by way of actuators receiving position setpoints formulated by equipment termed “flight controls” so as to maintain the aircraft in a given attitude, prescribed by the pilot or by an automated facility.
The flight controls constitute, together with the actuators, a first level of equipment which is distinguished from the other levels by the fact that it involves flight equipment indispensable to the pilot for acting on the aerofoils, flaps and engines. This first level of flight equipment is often supplemented with a second and a third level of flight equipment which consist of an automatic pilot/flight director and of a flight management computer facilitating the pilot's task and which are distinguished from the first level of flight equipment by the fact that the pilot could, strictly speaking, do without them.
The automatic pilot/flight director facilitates the pilot's task in the following of setpoints for heading, altitude, speed, etc. It operates in two possible ways: “flight director” operation where it indicates to the pilot, by way of viewing screens, the commands to be given to the flight controls so as to follow a setpoint and “automatic pilot” operation where it acts additionally on the flight controls so as to automatically follow the parametrized setpoint.
The flight management computer acts on the flight controls by way of the automatic pilot/flight director. It ensures various functions described in the ARINC 702 standard of December 1996 known by the name: “Advanced Flight Management Computer System”, including:                a function for inputting the summary definition appearing in the flight plan, for the route scheduled, that is to say of the string of waypoints linking the takeoff runway used at the departure airport to the landing runway scheduled at the destination airport with the overflight constraints associated with the waypoints and their scheduled overflight times as well as the departure and arrival procedures and optionally the air corridors (or “airways”) employed,        a function for formulating a 4D trajectory (Altitude+position+Speed) employing the route to be followed defined summarily in the flight plan while complying with the aircraft's performance and the flight constraints encountered along the 4D trajectory adopted, and        a guidance function engendering, by way of the automatic pilot/flight director, piloting commands and/or setpoints relating to the management of the thrust of the engines and of the aerodynamic configuration of the aircraft so as to follow the 4D trajectory formulated.        
During an approach phase preceding a landing, an aircraft generally descends from its cruising altitude to an intermediate altitude where it holds a deceleration pattern in the course of which it consumes its inertia until it reaches a speed compatible with a landing and aligns itself with the axis of the destination landing runway, on a descent plan allowing its wheels to touch down at the runway entrance. The trajectory of the approach phase as well as the speeds of traversal of the various portions of this trajectory often form the subject of regulation termed the runway approach procedure defined by a series of waypoints which lead to the entrance of the chosen runway and which are associated with local flight constraints (altitudes, speed, etc.).
The flight management computer, when it has been parametrized at the start of a mission with a flight plan comprising a destination landing runway approach procedure, can, once its guidance function has been activated, ensure the guidance of the aircraft in the course of this approach phase, by providing the automatic pilot/flight director with the commands necessary for on the one hand, reducing the speed of the aircraft while progressively altering its aerodynamic configuration (extension of the flaps, lift-enhancing slats, etc.) so as to preserve its lift and maintain its stability at low speed and on the other hand, fly past the waypoints imposed by the regulatory approach procedure while complying with the local flight constraints associated therewith.
As mentioned hereinabove, among the constraints that must be taken into account by the FMS of an aircraft, that which relates to the scheduled time of arrival at a given point of the flight plan with fixed termination, termed the RTA (“Required Time for Arrival”), depends on parameters such as the context of the air traffic control, termed ATC (arrival time slots, arrivals management system and airport management system, entry to zones of dense traffic), the workload of the pilots and the comfort of the passengers. Hereinafter in the text, the parameters, such as the aircraft flight speed and the waypoints of the aircraft, relating to this RTA constraint and making it possible to comply therewith, will simply be called the “RTA speeds”, “RTA points”, . . . while the RTA constraint will simply be called the RTA.
FIG. 1 presents the functional architecture of a conventional FMS 1. This is a computer which determines the geometry of the 4D profile (namely the 3 dimensions in space plus one time dimension speeds-profile). Such a system forms the subject of the ARINC 702 standard (Advanced Flight Management Computer System, December 1996). It ensures all or some of the following functions:                navigation (LOCNAV) 2, for performing optimal location of the aircraft as a function of the means SL of geo-location (GPS, GALILEO, VHF radio beacons, inertial platforms);        flight plan (FPLN) 3, for inputting the geographical elements constituting the skeleton of the route to be followed (departure and arrival procedures, waypoints, aerial routes;        navigation database (NAV DB) 4, for constructing geographical routes and procedures with the help of data included in the bases (points, beacons, interception or altitude “legs”, etc.);        performance database (PERF DB) 5 containing the aerodynamic parameters and the characteristics of the engines of the craft;        lateral trajectory (TRAJ) 6: for constructing a continuous trajectory on the basis of the points of the flight plan, complying with the aircraft performance and the confinement constraints (RNP);        predictions (PRED) 7: for constructing a vertical profile optimized on the basis of the lateral trajectory;        guidance (GUIDANCE) 8: for guiding the aircraft in the lateral and vertical planes on its 3D trajectory, while optimizing the speed. It is linked, if appropriate, to an automatic pilot 9;        digital data link (DATALINK) 10: for communicating with the control centres and other aircraft (C-A).        
The flight plan is entered by the pilot with the aid of a man-machine interface 11 (or through a data link termed “Datalink”) with the help of the data contained in the navigation database 4. This plan comprises a succession of segments called “legs” which are formed of a termination and of a geometry (turn, great circle, rhumb line, etc.). These “legs” are standardized at the international level in an AEEC document (ARINC 424).
The pilot then enters the parameters of the aircraft: weight, set of cruising levels, one or more optimization criteria (type of performance, etc.). This information thus entered into the FMS allows the TRAJ and PRED modules to compute respectively the lateral trajectory and the vertical profile (altitude/speed) minimizing the cost according to given criteria.
Current FMS systems, although comprising the functions listed hereinabove, do not make it possible to establish an optimal planning of trajectory of the predictions and of guidance to take account of a flypast and arrival time constraint. Indeed, in these current FMS systems, the trajectory planning calls upon schemes based on the pre-existence of a “cost index” table (time/fuel cost ratio) and upon a limited adaptation of the speeds profile in the climb and descent phases (see for example U.S. Pat. No. 5,121,325) or on a readjustment of the ground speeds “leg” by “leg” (see for example patent US 2003-6507782), based on a trajectory computation as a function of wind and speed. The drawbacks of such systems are: the non-optimization of the time authority on the mission if using the “cost index”, the total dependency of the method in relation to the pre-existence of the said “cost index” table, the generation of numerous different speed segments when using “leg” by “leg” optimization and the non-precision of the system based on the “legs” when these exist in small number in the flight plan.